# Physics as it Relates to Pedalling a Bike

1. Mar 16, 2009

### Ratfish

Hi, I was discussing cycling with my dear friend, Tim, and in no time at all we were at loggerheads with regard to weight savings as it relates to performance increases. Tim is of the opinion that "mass is mass" no matter where on the bike/person it is (controlling for aerodynamics etc.) but I am of the opinion that mass in certain places actually inhibits one's cycling ability much more than if the mass were in another location.

One example that I thought of was the mass of the crank arms, pedals, and shoes of the rider. A typical fit cyclist is probably cruising along the road at a pedalling cadence of, let's say, 100 rpm. The "rotational velocity" of the pedals, or whatever your might call it, isn't usually static as a person is probably accelerating and decelerating constantly, but even if it was, it seems to me that a person is needing to perform more work to rotate that extra mass around its axis than if the weight were, for example, located on Tim's not insubstantial gut.

Another option, I suppose, is that the force of gravity acting upon the front pedal's mass balances out the extra work needed to fight gravity on the way up for the opposing pedal.

The point of the discussion is that weight savings in cycling is an expensive endeavor where one may pay dearly for a savings of only a few grams. Those grams, when examined in relation to the mass of the rider as a whole do not seem to be all that consequential, unless they are somehow "heavier" in certain spots than they are in others, i.e. the crank arms etc.

Could anyone enlighten us further?

2. Mar 17, 2009

### rcgldr

In the case of a very thin hoop, which the wheel and tire approximate, the effective momentum is doubled. 1 gram of tire mass equals 2 grams of frame mass in terms of the effect on acceleration.

3. Mar 17, 2009

### skeleton

Static weight is predominately relevant when climbing a hill on a bike. Rotational weight is relevant when accelerating.

Beyond weight, other factors are crucial - perhaps even more so. The most, IMHO, is stiffness. The stiffness of a bike's frame, forks and cranks have a significant effect on how much of the cyclist's energy is preserved and transferred to locomotion. For this factor, some extra weight may be tolerable for the greater benefit of increased stiffness. (Of course, a stiffer bike is often less comfortable which impacts the efficiency of the cyclist but not that of the bike itself.)